Observing with the international baselines of LOFAR opens up the domain of sub-arcsecond imaging of the sky at metre wavelengths.
Resolutions of order 0.3 arcseconds with sensitivity <<1mJy/beam are possible at the low end of the HBA frequency range. However, the present uv coverage of international LOFAR, combined with potentially large a-priori amplitude calibration uncertainties, mean that sources with significant extended structure are challenging to calibrate and map.
Calibration is the greatest challenge for long baseline LOFAR observations, because of the extreme scarcity of bright, compact sources with simple structure.
This situation is exacerbated by the large impact of differential ionospheric effects, which limits the amount of averaging that can be performed in frequency and in time.
Imaging can also present difficulties due to the wide field of view, which results in very large numbers of pixels if the entire FOV is to be sampled at the full resolution. On the other hand, the high resolution means that individual sources are separated by very many beams, which can simplify the imaging process. Individual images of small fields centred on known sources can be made from averaged data. For bright sources imaged in this way it should be possible to achieve high dynamic range without imaging the whole field, as is needed for observations using only the Dutch component of LOFAR.
The information provided here is intended to aid correct scheduling of International LOFAR observations; instructions on reducing the data are provided elsewhere.
The greatest possible sensitivity for calibration is obtained in two ways:
1) Phasing the core stations using a post-correlation summation of the visibilities. This provides a single sensitive station which can be used as a reference for calibration. In order to calibrate the core for phasing, "normal" LOFAR calibration approaches can be utilised (either beam switching with the full bandwidth over timescales of many minutes, or contemporaneous calibration using a fraction of the bandwidth in a second station beam positioned on a bright calibrator source). A good source for calibration of the core stations will have a flux density 10 Jy (more in the LBA band) and be compact on arcminute scales. It need not be extremely close on the sky to the target.
2) Fringe fitting (solving for delay [derivative of phase with frequency] and rate[derivative of delay with time]) on the target itself or a very nearby compact calibrator source. This coherently adds visibilities across frequency and time, assuming the phase change with frequency and time is linear. In actuality, the ionospheric delay changes with frequency (quadratic change of phase), but it can can be assumed to be constant over a reasonably narrow bandwidth.
In general night time observing should be used if possible to ensure that the delays and rates caused by ionospheric changes are minimized, although the specific ionospheric conditions at the time of the observation can vary much more than the average difference between night and day.
Assuming that the core stations are phased and the data is arranged into spectral windows of width ~3 MHz, the required flux density for calibration is of order 100 mJy (on the longest baselines) for HBA observations. This uses a solution interval of order 1 minute. The LBA is of order 20x less sensitive, so a flux density of ~2 Jy is required. These numbers are derived from current (July 2014) array performance and may improve somewhat if station calibration is improved further. Rampadarath, Garrett & Polatidis (2009) contains a list of potentially suitable calibrators.
The above critical flux density must be present on all baselines within the target itself, or within a nearby calibrator with simple structure to whose phase solutions can be transferred to the potentially weaker / more complex target source. Given the present uncertainties in amplitude calibration in order for fringe-fitting and imaging to work for long baseline LOFAR the source used for fringe detection and calibration should either be simple (close to point-like) or have an existing good starting model at similar angular resolution. If neither the target nor any nearby potential calibrator source fulfills the requirement for simple or known structure, a short scan should be included at some point in the observation on a more distant source which does satisfy this criterium, preferably at high elevation. In this case, producing a lower resolution image of the source to be used as a calibrator using only the Dutch array as a starting point is also recommended.
Transfer of calibration phase has been demonstrated within a single station beam over angular separations of ~0.5 degrees in the HBA. Transfer of calibration over an angular separation of 0.75 degrees has been shown to work under good observing conditions at HBA frequencies, but this is not expected to be always successful. Transfer of calibration over a separation of 1 degree or more will often not result in significant improvements in coherence time. The success of spatial calibration transfer will be heavily dependent on ionospheric conditions, and the expected conditions are not yet well characterised for international baselines. A separate station beam at identical frequencies can be placed on the calibrator object - transfer of calibration between station beams has been demonstrated. However, since the calibrator will necessarily fall within the station field of view if it is to be useful anyway, this approach is generally not useful for calibrating the international stations. The continuous monitoring of a calibrator is recommended -- beam switched phase referencing (i.e., time interpolation) has not yet been demonstrated.
The computational power required for calibration for a single pointing direction (including core phasing, format conversions and calibration itself) is not unreasonable, requiring 50-100% of observe time on a fraction of the CEP2 cluster. Differential phase--only calibration on a second or subsequent source is considerably faster, requiring only a small fraction of observe time on a single node.
Data for International LOFAR is generally taken with 64 channels/subband and 1 second averaging. For HBA this allows for a field of view of approximately 1 degree radius (predominantly limited by time smearing). Generally, the first step of any data processing will be flagging and averaging. Typical post-averaging values used with International LOFAR observations are 4 channels/subband and 4 seconds. This limits the field of view to about 10 arcminutes radius for the HBA (predominantly limited by bandwidth smearing). This is less restrictive than the "station beam" of the phased core, which with an effective diameter of 2 km has a beam width of around 4 arcminutes. To image sources further away from the phase centre, it is necessary to go back to the raw data, shift to a new tangent point using NDPPP, average again and then apply the calibration derived from the calibrator phase centre. The time taken for NDPPP to uvshift and average a dataset is considerably less than the time taken for NDPPP to flag a dataset, so if multiple widely separated tangent points will be required, a flagged but unaveraged dataset should be generated by once NDPPP and then shifted/averaged multiple times.
For HBA observations the required pixels size is approximately 0.1 arcseconds, and a 1024×1024 pixel image can be made without suffering from w-projection effects, so it is possible to directly image the whole smearing limited FOV in one pass using around 100 facets in e.g. AIPS. Alternatively, one can image using a w-projection capable imager like CASA, and then it is possible to make a single large image (e.g., 8192×8192) but this is likely to be slow. Of course, it is also possible to uv shift to areas of interest within the 20'x20' FOV and image a smaller region. In this case, bright sources should be imaged first and subtracted. Imaging a single facet is fast, taking a small fraction of observe time. Imaging the entire smearing-limited FOV of the averaged data using either faceting or w-projection techniques is considerably more computationally intensive.
Some of the processing steps described above are part of a pipeline performed manually by advanced users. This also involves software packages that are not part of the LOFAR software (e.g. AIPS).
pre-process the data (i.e. flagging, demix (if needed), and averaging),
average the calibrator data (e.g. 1ch,8secs),
perform amplitude calibration on the averaged calibrator data,
apply the solutions to the target.
Optionally, it also performs a (phase-)shift of the source and sums the core stations to form a single phased core station, filtering out the now redundant core stations.
Computational Requirements for the Standard Long Baseline Pipeline
In order to present practical estimates for the Processing over Observing time ratio (P/O ratio) a characterisation of the pipeline performance was performed with the parameter space defined by: the array mode (HBA), the number of channels (64), the integration time (1sec), the number of sub-bands (20). Tests indicate a systematic larger value of the P/O ratio for the amplitude calibration of the calibrator than the target and phase shift steps, the overall P/O ratio of the all steps being about 4.